Pretzel orbit design with asymmetric lattice (v20140930) Huiping Geng CEPC Accelerator Physics regular meeting 2015.10.23

Review of asymmetric lattice (v20140930) Circuference: 54.752 km FODO cell length: 47.2 m Phase advance per cell: 60/60 degrees ARC length:5852.8m= (2+120+2)*47.2 Short straight: 18 FODO cells, 849.6m Long straight: 24 FODO cells, 1132.8m Results reported in HF2014 are using this lattice.

Issues with pretzel orbit For ideal pretzel orbit, the following relationship should be fullfilled: i.e. the phase advance between parasitic crossing point should be a integer number of 2*Pi. For our lattice, it is comprised of 60/60 degree FODO cells, so the relationship can be written as: But for this asymmetric lattice, as for 50 bunches case: This is why we say pretzel orbit is not working for this lattice version.

To make it work Two options(assuming phase advance per cell keeps constant): Change the cell length, which will result in the change of emittance, circumference etc. Change the circumference In the following, we take the easy way, i.e. we change the circumference to make the lattice work for pretzel orbit of 50 bunches

Changes made ARC length:5852.8m Short straight: 18 FODO cells, 849.6m Long straight: 34 FODO cells, 1604.8m Circumference: 56.640km After making this chang, every nearest parasitic collision points will have a phase advance of 4Pi.

Comparison of results before adding pretzel v20140930 New version v20150923

Pretzel orbit design Find proper positon and strength of static electric separators, then the pretzel orbit can be well generated.

Pretzel orbit effect on lattice

Pretzel orbit effect correction 选择第一个弧区第三个FODO入口（消色散节出口）为初始条件，以6个FODO cell为周期， 重新匹配周期解

Pretzel orbit effect correction 第一个弧区消色散条件重新匹配，消色散点选择在第二个静电分离器出口，beta函数满足周期解匹配。

Pretzel orbit effect correction 第二个弧区需要重新匹配，因为SEP1止SEP3的相移不是2Pi整数倍。是否可以增加相移条件使弧区1和2的SEP1止SEP3的相移满足2Pi整数倍？ 选择第二个弧区第三个FODO入口（消色散节出口）为初始条件，以6个FODO cell为周期， 重新匹配周期解

Pretzel orbit effect correction 第二个弧区消色散条件重新匹配，消色散点选择在此弧区的第二个静电分离器出口，beta函数满足周期解匹配。

Pretzel orbit effect correction 校正后的全环lattice，调整色品矫正后，需将上述过程重复，寻找新的匹配条件。

Pretzel orbit effect correction

导入sad 静电分离器强度设置为0

静电分离器与kick的差别 给定入口参数 周期解

Summary Pretzel orbit issue has been fixed by changing the circumference of the ring But the change of drift space length will have a big effect on dynamic aperture (as we have already noticed), which will need further study. MAD and SAD does not agree…